In simplest form, a radar system consists of the generation of a pulse having a certain duration, followed by a listening period in which returns are received. A radar designer usually wishes to increase the power of target returns to provide better detection. The most straightforward way to do this is to increase pulse amplitude. Unfortunately, useful radars require pulse amplitudes that would result in waveguide arcing and electrical breakdown. A conventional way to circumvent this problem is to use pulse compression techniques, i.e. transmitting a series of low amplitude pulses (subpulses) of the same aggregate energy as a higher amplitude pulse. The pulses are typically modulated (the modulated pulse also called a coded waveform) and transmitted. Returns are processed through a matched filter (i.e. a filter whose transfer function optimizes the signal to noise ratio), resulting in a signal that is a compressed pulse that is also the auto-correlation of the coded waveform in the absence of doppler shifts. Pulse coding can be expressed in matrix form, examples of which are matrices for the well-known Frank and P4 codes. The matrix describes the phase shifting necessary to phase modulate the subpulses of a coded pulse. Such a matrix is a square one of dimension NxN, each element of which represents a phase shift (the phase modulation) of one subpulse. The Frank or P4 code consists of concatenated N.sup.2 subpulses having the phases described by the elements of the consecutive rows of the matrix, reading from left to right. An example of a Frank matrix is shown in FIG. 1 for N=4. The elements of, e.g., the second row, 1, j, -1, -j, describe the fifth to eighth subpulses with respective phase modulation of 1 (i.e. 0.degree.), j (i.e. 90.degree.), -1 (i.e. 180.degree.), and -j (i.e. -90.degree.).
Such a radar system commonly operates by generating a sequence of identically coded waveforms, separated in time by detection, or listening intervals, in which the radar can detect returns of the transmitted waveform. The range for which the radar can receive unambiguously is limited to the distance a pulse can travel to and from the radar during its detection interval. This distance is called the unambiguous range. Often, downrange from the unambiguous range is clutter (e.g. hills) which can reflect radar returns, and such clutter can cause pulses to return to the radar during detection intervals for later pulses (i.e. be "folded over" into a later detection interval). Clutter causing foldover into the next pulse's detection interval is said to be located in the first ambiguous range, foldover into the second succeeding detection interval is said to be from the second ambiguous range, etc. Unambiguous range clutter is undesirable because it increases the cancellation requirements of the radar and the dwell time required to process clutter returns, and because it causes the range to be ambiguous in mapping applications.
In Statutory Invention Registration (SIR) H767, the inventors disclosed a method and apparatus for eliminating ambiguous range clutter. The invention of SIR H767 derives from a discovery by the inventors of properties of the Frank and P4 matrices, in particular that the sum of cross-correlations between rows of a Frank or P4 matrix, spaced by a constant number of rows, is zero. More generally, for such a matrix of dimension NxN, if the cross-correlations between rows q and m of the matrix are given by C.sub.qm (i), for i=.+-.0, .+-.1, .+-.2, . . . , .+-.(N-1): ##EQU1## where m=(q+r) mod N, r=1, 2, . . . , (N-1).
The invention of SIR H767 is a method and apparatus for transmitting and processing a sequence of coded pulses F.sub.1, F.sub.2, . . . , F.sub.N-1, F.sub.0, F.sub.1, . . . , F.sub.N-1, each of the coded pulses F.sub.n, n=0, 1, 2 . . . , N-1, being coded in accordance with the (n+1)th row of a Frank or P4 matrix of dimension NxN. Each of the coded pulses are spaced from adjacent ones of the coded pulses by time intervals t.sub.0, t.sub.1, . . . , t.sub.n-1, each F.sub.n being followed immediately by a corresponding t.sub.n, the last N of said time intervals being denominated detection intervals. An integer c is selected from the set whose members are: 0, 1, 2, . . . , N-1. Returns of the coded pulses during each of the detection intervals are detected. The returns detected in each detection interval are passed through a corresponding filter matched to one of the coded pulses F.sub.n, n=(N+j-c) mod N, where j=0, 1, 2, . . . , N-1. The outputs of the filters generated during all N detection intervals are coherently summed.
The importance of this scheme derives from the inventors' discovery that the cross-correlations of rows of Frank or P4 matrices spaced equally apart sum to zero. In most simple form, such a system is designed to generate a series of pulses F.sub.0, F.sub.1, F.sub.2, . . . , F.sub.n-1. After each pulse the system processes returns using a filter matched to the pulse, changing the filter with each detection interval. Thus over all the detection intervals the system employs a sequence of filters matched to the various pulses F.sub.n, and employs them in the same order as the pulses to which they are matched. Each value of c shifts the filter sequence in a circular manner, and clutter time shifts the returns an amount determined by the particular ambiguous range in which the clutter is situated. If these shifts are identical, each returning pulse in each interval is matched to the filter employed, and the detected signal in each interval is the auto-correlation of the filter's transfer function. The coherent sum of these auto-correlations over the detection intervals yields the compressed pulse. If the shifts are not identical, the detected output in each interval is the cross-correlation of the pulse and the transfer function of the filter. Because the pulses are coded sequentially according to rows of a Frank or P4 matrix, and because the filters are not matched to these pulses in this sequence, the coherent sum of these over the detection intervals constitute the sum of cross-correlations between rows of the coding matrix spaced a constant amount apart. The inventors' discovery about Frank or P4 matrices demonstrates that this sum is zero.
Thus by choice of c a system according to the invention can "tune" itself to detect returns from the unambiguous range, or any of the ambiguous ranges, and reject all other returns. One could also have a plurality of these systems, each tuned to one range, and thus detect all returns and simultaneously determine from which range each return has come.
However, the invention disclosed in SIR H767 is limited to use with a Frank or P4 code. This limits the freedom an engineer has in designing radar systems which have the advantages of that invention. Also, with the Frank or P4 code even small doppler shifts from ambiguous range echoes can be detected, causing false alarms.